Plaka and Monastiraki neighborhoods put you within walking distance of the Acropolis and most major sights — the most logical base. Koukaki (just south of the Acropolis) is trendier and slightly cheaper, with excellent cafes and restaurants. Psiri is the nightlife district. Kolonaki is upscale and stylish, near the National Archaeological Museum and Lycabettus Hill.
Rooftop hotels with Acropolis views are a genuine Athens USP — even budget hotels sometimes have spectacular roof terraces. Syntagma Square hotels are central for business but uninspiring. Book well ahead for late April–May and September–October, when Athens fills with European visitors.